Document U.S. Pat. No. 6,780,167 discloses a connection device for a system for administering medical treatment fluids, comprising:                a connection member comprising a primary flow channel and secondary flow channels, each flow channel comprising a proximal aperture intended to be fluidically connected to a respective medical treatment fluid administration tube and a distal aperture, and        a connection endpiece intended to be connected to a catheter, the connection endpiece comprising a mounting portion in which the connection member is mounted, the connection member and the connection endpiece delimiting an internal chamber into which open the distal apertures of the primary and secondary flow channels, the connection endpiece further comprising an outlet orifice opening into the internal chamber.        
During the use of such a connection device, the fluids flowing inside the primary and secondary flow channels mix in the internal chamber before being administered to the patient. Such mixing may be disadvantageous, in particular when the fluids from the different flow channels are incompatible and may precipitate. In fact, mixing of such fluids may lead to unsuitable treatment for the patient.
In order to avoid mixing of the fluids from the primary and secondary flow channels, it is known from document US 2008/0105318 to position the distal aperture of the primary flow channel between the distal apertures of the secondary flow channels, form a guide ribs inside the internal chamber, and configure the internal chamber such that its distal end has a diameter larger than that of its proximal end.
Such a connection device has a complex connection endpiece and requires a specific arrangement of the different flow channels. Furthermore, such a connection device requires a primary flow channel with a large cross-section so as to avoid any mixing of the fluids coming from the secondary flow channels, which requires a significant flow rate of the fluid flowing in the primary flow channel.